OMG - BEN WAS FLUNG FROM THE SEAT! -
The Coal Cracker is a 37 year old ride at Hershey Park, Pennsylvania. As a hydroflume boat ride, the coal cracker carries up to 150 people to the top of a 49 ft high drop and launching down at 35 mph! The coal cracker was one of the first rides built in the park and to this day is still rated as a 4 of 5 degree thrill ride. It is one of the most beloved rides in the park and is meant for all ages, excluding hand held infants. In this experiment, technology was used to measure and record the motion of the coal cracker's final hill fall. Acceleration, velocity and conservation of energy were calculated and compared to the values listed on the official Hershey website.
- Finding the angle of the drop. This was found using a protractor and basing it off of the angle formed at the middle right of the picture. It showed that the angle of the hill was approximately 30 degrees.
- Analyzing the ride. This picture shows how logger pro was used to analyze the video. The points are in blue, plotted following the flume down the hill. Also the height of the hill was found in this picture, and the origin is shown as well. Altogether, the acceleration, position, velocity, and height of the hill were all found from this video. The scale used in this video was the distance from the front of the flume to the back, found out by taking a picture of Ben standing beside one of the flumes below: - Finding the length of the Plume Boat. Ben's height of 5 ft 8.5 inches was used as a scale here in order to determine what the distance was from the front of the flume to the back.
Angle of Hill - 30 Degrees
Length of Boat - 2.254m
Verifying that the instantaneous velocity at the bottom of the hill is the same as the Hershey Park website statistic of the Coal Cracker.
X instantaneous velocity at the bottom of the hill = 8.881 m/s
Y instantaneous velocity at the bottom of the hill = 12.543 m/s
Total velocity at bottom of hill = 8.881^2 + 12.543^2 = sqr(236.199) = 15.37m/s = 34.38mph = 1.77 percent error compared to 35 mph average on Hershey Park website statistics.
Verifying that everything falls at the same rate, 9.8 m/s^2
In this case, the hill is at an angle of 30 degrees, so the acceleration due to gravity is affected by the hill. This is taken care of with sine! As seen below:
9.8*sin30 = 4.9 = acceleration down hill. (Hill at 30 degrees)
X calculated acceleration from the best fit line of velocity graph above= 3.894
y calculated acceleration from the best fit line of velocity graph above= 2.733
Total acceleration = 3.894^2+2.733^2 = sqr(22.63) = 4.76 m/s^2
Percent error = 2.86 percent error compared to 4.9 m/s^2 which is what the acceleration due to gravity should be on the hill.
Conservation of energy (E1 = E2)
E1 is when the plume at the top of the hill and E2 is when the plume was at the bottom of the hill.
(At top of hill) - mgy+1/2mv^2 = (At bottom of hill) 1/2mv^2
9.8*12.69+1/2*((1.033^2+.127^2)^.5)^2 = 1/2*15.37^2 (Total velocity at bottom of hill) =
^x instantous velocity of plume^2 + y instantaneous velocity of plume^2 = total velocity of plume at top of hill^2
124.9 = 118.12, Percent difference between the two energies = (124.9-118.12/((124.9+118.12)/2) = 5.58 percent difference
^ E1-E2/Eaverage
The Coal Cracker is a 37 year old ride at Hershey Park, Pennsylvania. As a hydroflume boat ride, the coal cracker carries up to 150 people to the top of a 49 ft high drop and launching down at 35 mph! The coal cracker was one of the first rides built in the park and to this day is still rated as a 4 of 5 degree thrill ride. It is one of the most beloved rides in the park and is meant for all ages, excluding hand held infants. In this experiment, technology was used to measure and record the motion of the coal cracker's final hill fall. Acceleration, velocity and conservation of energy were calculated and compared to the values listed on the official Hershey website.
Angle of Hill - 30 Degrees
Length of Boat - 2.254m
Verifying that the instantaneous velocity at the bottom of the hill is the same as the Hershey Park website statistic of the Coal Cracker.
X instantaneous velocity at the bottom of the hill = 8.881 m/s
Y instantaneous velocity at the bottom of the hill = 12.543 m/s
Total velocity at bottom of hill = 8.881^2 + 12.543^2 = sqr(236.199) = 15.37m/s = 34.38mph = 1.77 percent error compared to 35 mph average on Hershey Park website statistics.
Verifying that everything falls at the same rate, 9.8 m/s^2
In this case, the hill is at an angle of 30 degrees, so the acceleration due to gravity is affected by the hill. This is taken care of with sine! As seen below:
9.8*sin30 = 4.9 = acceleration down hill. (Hill at 30 degrees)
X calculated acceleration from the best fit line of velocity graph above= 3.894
y calculated acceleration from the best fit line of velocity graph above= 2.733
Total acceleration = 3.894^2+2.733^2 = sqr(22.63) = 4.76 m/s^2
Percent error = 2.86 percent error compared to 4.9 m/s^2 which is what the acceleration due to gravity should be on the hill.
Conservation of energy (E1 = E2)
E1 is when the plume at the top of the hill and E2 is when the plume was at the bottom of the hill.
(At top of hill) - mgy+1/2mv^2 = (At bottom of hill) 1/2mv^2
9.8*12.69+1/2*((1.033^2+.127^2)^.5)^2 = 1/2*15.37^2 (Total velocity at bottom of hill) =
^x instantous velocity of plume^2 + y instantaneous velocity of plume^2 = total velocity of plume at top of hill^2
124.9 = 118.12, Percent difference between the two energies = (124.9-118.12/((124.9+118.12)/2) = 5.58 percent difference
^ E1-E2/Eaverage